Final Exam Physical Chemistry 1998
X-ray Section.
1. A solution of carbon in fcc iron has a density of 8.105 g/cm3 and a unit cell edge of 358.3 pm. a) What is the density of pure iron in this form? b) Are the carbon atoms interstitial or do they substitute for iron atoms in the lattice? EXPLAIN.
First Law and Gases.
2. a) Derive the equation for the heat of a reversible, isothermal expansion of one mole of an ideal gas from P1 to P2.
b) Calculate q, w, DU involved in the reversible isothermal compression of 2 moles of He (Cv = 1.5R) from 0.24 bar to 3.65 bar at 15 oC. (Assume an ideal gas).
First Law and Chemical Reactions.
3. The vaporization of HCl(l) at its normal boiling point of -85 C at 1 bar pressure and is accompanied by the absorption of 16.15 kJ/mol. For vaporization of one mole of HCl at -85 C and 1 bar, calculate q, w, DHo DUo, and DSo.
.
Second Law Section.
4. 600 J of heat is irreversibly transferred from a hot object at 600 K to a cold object at 300 K.
a) Calculate the total change in entropy of the process.
b) Explain how this relates to the second law.
c) calculate the maximum work that could be obtained from this transfer of heat in a heat engine operation at these two temperatures and explain in terms of both the first law and the second law.
Second Law and Free Energy
5. a) Calculate the DrHo and DrSo at 25 oC for the reaction
7 H2(g) + 2 NO2(g) = 2 NH3(g) + 4 H2O(g)
b) Calculate the DrGo at 25 oC for the reaction from both the DrHo and DrSo and from the DfGo's.
Free energy.
6. The density of water and ice are respectively, 1.000 g/cm3 and 0.917 g/cm3. Its heat of fusion is 6.008 kJ/mol. Calculate the pressure it would take in bar or atm or kPa to lower the m.p. of ice, 0.5oC.
7. When a chemical reaction was studied at 27oC and 37o, the experimentally determined equilibrium constants were 2.3x10-6 and 5.1x10-6, respectively.
Calculate the DrGo ,DrHo , and DrSoat 27 oC for the reaction.
Solutions Section.
8. Calculate the DGo of reaction:
AgCl(s) = Ag+(aq) + Cl-(aq)
From
a) the free energies of formation in the following table:
| DfHo kJ/mol | DfGo kJ/mol | So J/K-mol | |
| Ag+(aq) | 105.579 | 77.107 | 72.68 |
| Cl-(aq) | -167.159 | -131.228 | 56.5 |
| AgCl(s) | -127.068 | -109.789 | 96.2 |
b) from the cell potentials:
| Ag+|Ag | 0.7992 v |
| Cl-|AgCl(s)|Ag | 0.2224 v |
c) from Ksp = 1.8x10-10
Derivations
9. a) Derive the equation, dG = -SdT + VdP starting with the first law of thermodynamic and the definitions of enthalpy and free energy for a reversible process in which only pressure volume work is done.
b) Derive the equation
()p = - DSo
from the equation in part a). Explain the derivation.
10. Derive the osmotic pressure equation PV = nRT and indicate clearly what V and n are (what volume? moles of what?)